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On three welfare properties of monopoly in bilateral exchange

Author

Listed:
  • Busetto, Francesca
  • Codognato, Giulio
  • Ghosal, Sayantan
  • Turchet, Damiano

Abstract

We establish three welfare properties of the model of monopoly introduced by Busetto et al. (2023), where one commodity is held only by the monopolist, represented as an atom, and the other is held only by small traders, represented by an atomless part. First, we prove that a monopoly allocation is Pareto optimal if and only if it is an allocation which corresponds to an efficiency equilibrium. Second, we reformulate a paradox, due to Shitovitz (1997), to show that for any monopoly allocation there is another core allocation, distinct from both a monopoly allocation or a Walras allocation, which is, utility-wise, advantageous for the monopolist and nonadvantageous for the small traders. Finally, we prove a theorem which shows that monopoly is advantageous for the monopolist and nonadvantageous for each trader in the atomless part with respect to all Walras allocations which are not monopoly allocations.

Suggested Citation

  • Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Turchet, Damiano, 2025. "On three welfare properties of monopoly in bilateral exchange," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    • Handle: RePEc:eee:mateco:v:119:y:2025:i:c:s0304406825000643
    DOI: 10.1016/j.jmateco.2025.103147
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    References listed on IDEAS

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    1. Daniel M. Schydlowsky & Ammar Siamwalla, 1966. "Monopoly Under General Equilibrium: A Geometric Exercise," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(1), pages 147-153.
    2. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890, December.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "On the foundation of monopoly in bilateral exchange," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1261-1290, December.
    4. Houshang H. Sohrab, 2014. "Basic Real Analysis," Springer Books, Springer, edition 2, number 978-1-4939-1841-6, December.
    5. Benyamin Shitovitz, 1997. "A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 559-563.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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    Keywords

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    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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